5 papers
Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence
Vestislav Apostolov, Brent Pym, Jeffrey Streets
We introduce a notion of K-polystability for compact Kähler holomorphic Poisson manifolds. On the one hand, this notion of stability is well-adapted to constructions of moduli spa…
Formal structure of scalar curvature in generalized Kähler geometry
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
Building on works of Boulanger and Goto, we show that Goto's scalar curvature is the moment map for an action of generalized Hamiltonian automorphisms of the associated Courant alg…
Rigidity results for non-Kähler Calabi-Yau geometries on threefolds
Vestislav Apostolov, Giuseppe Barbaro, Kuan-Hui Lee +1
We derive a canonical symmetry reduction associated to a compact non-Kähler Bismut-Hermitian-Einstein manifold. In real dimension , the transverse geometry is conformally Kähl…
Toric geometry of generalized Kähler-Ricci solitons
Vestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets +1
We establish a local equivalence between toric steady Kähler-Ricci solitons and -type toric generalized Kähler-Ricci solitons (GKRS). Under natural global conditions we show t…
The generalized Kähler Calabi-Yau problem
Vestislav Apostolov, Xin Fu, Jeffrey Streets +1
We formulate an extension of the Calabi conjecture to the setting of generalized Kähler geometry. We show a transgression formula for the Bismut Ricci curvature in this setting, w…